# Chapter Three-Activity Cost Behavior20104611037

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```					                Hansen, Mowen, Elias & Senkow (ITP, 1998)

Chapter 3 - Activity Cost
Behaviour

Chapter 3-1
Hansen, Mowen, Elias & Senkow (ITP, 1998)

Learning Objectives

   Define and describe cost behaviour and
explain the role of the resource usage model
in understanding cost behaviour.
   Separate mixed costs into their fixed and
variable components using the high-low
method, the scatterplot method, and the
method of least squares.
   Evaluate the reliability of a cost equation.
   Explain the role of multiple regression in
assessing cost behaviour.
   Describe the use of managerial judgement in
determining cost behaviour.
Chapter 3-2
Hansen, Mowen, Elias & Senkow (ITP, 1998)

Basic Terms - 1

   Activity capacity: the ability to perform
activities
   Practical capacity: the efficient level of
activity performance
   Resources: economic inputs that are
consumed in performing activities
   Resource spending: the cost of acquiring
capacity to perform an activity
   Resource usage: the amount of activity
capacity used in producing the activity output

Chapter 3-3
Hansen, Mowen, Elias & Senkow (ITP, 1998)

Basic Terms - 2

   Resources supplied as used and needed:
these are resources that are acquired from
outside sources, where the terms of
acquisition do not require any long-term
commitment for any given amount of the
resource. Examples: materials & energy
   Resources supplied in advance of usage:
these are resources acquired by the use of
either an explicit or implicit contract to obtain
a given quantity of resource, regardless of
whether the quantity of the resource available
is fully used or not.

Chapter 3-4
Hansen, Mowen, Elias & Senkow (ITP, 1998)

Cost Behaviour
Fixed Costs Behaviour                    Variable Cost Behaviour

\$                                  \$
Relevant Range

Activity                                    Activity

Unit Cost Varies with Volume            Unit Cost Rate is Constant

Chapter 3-5
Hansen, Mowen, Elias & Senkow (ITP, 1998)

Total versus Average Variable Cost

Example:
Suppose that Porter Pottery Company makes
mugs. Each mug requires 1/4kg. of clay at \$2
per kg. If Porter manufactures 5,000 mugs,
the total cost of clay is \$2,500 (5,000 x \$2 x
.25). If Porter manufactures 10,000 mugs, total
cost of clay is \$5,000 (10,000 x \$2 x .25). The
average cost of clay per mug stays at \$0.50
(.25 x 2) no matter how many mugs are made.

Chapter 3-6
Hansen, Mowen, Elias & Senkow (ITP, 1998)

Total versus Average Variable Cost

Total Variable Cost

Cost                                           TVC = \$.5X

\$5,000

\$2,500

5,000             10,000
Mugs
Chapter 3-7
Hansen, Mowen, Elias & Senkow (ITP, 1998)

Total versus Average Variable Cost
(continued)

Average Variable Cost
Cost

\$0.50                                      AVC = \$0.50

5,000           10,000
Mugs
Chapter 3-8
Hansen, Mowen, Elias & Senkow (ITP, 1998)

Total Fixed versus Average Fixed Cost

Total Fixed Cost
Cost
\$1,500                                        Year 2

\$1,000                                        Year 1

\$500

Activity Level

Chapter 3-9
Hansen, Mowen, Elias & Senkow (ITP, 1998)

Total Fixed versus Average Fixed Cost
(continued)

Total versus Average Fixed Cost

Cost

TFC
AFC

Activity Level

Chapter 3-10
Hansen, Mowen, Elias & Senkow (ITP, 1998)

The Behaviour of Mixed Costs
Linearity Assumption

Total Costs

\$Cost
Fixed Costs
Variable Costs

Number of Units Produced
Total Costs = Fixed Amount + Variable Cost Per Unit x Number of Units
= Fixed Costs + Variable Costs
Y = F + V(X)
Y= Total mixed costs (the dependent variable)
(X) = Cost Driver or Independent Variable
Chapter 3-11
Hansen, Mowen, Elias & Senkow (ITP, 1998)

Step Variable Costs
Linearity Assumption

Narrow Width
\$Cost

Number of Units Produced

Chapter 3-12
Hansen, Mowen, Elias & Senkow (ITP, 1998)

Types of Fixed Costs

Committed Fixed Costs
Discretionary Fixed Costs
Step Fixed Costs

Chapter 3-13
Hansen, Mowen, Elias & Senkow (ITP, 1998)

Step Fixed Costs
Linearity Assumption

\$Cost

Normal Operating
Range (Relevant Range)

Number of Units Produced

Chapter 3-14
Hansen, Mowen, Elias & Senkow (ITP, 1998)

Methods for Separating Mixed
Cost Into Fixed and Variable
Components
The High-Low Method
Scatterplot Method
The Method of Least Squares

Chapter 3-15
Hansen, Mowen, Elias & Senkow (ITP, 1998)

Mixed Costs: An Example
Month      Utility Costs              Unit Produced
January     \$2,000                       200
February      2,500                     400
March         4,500                      600
April         5,000                      800
May          7,500                     1,000

Chapter 3-16
Hansen, Mowen, Elias & Senkow (ITP, 1998)

The High-Low Method
Variable Cost Rate = (Y2 - Y1)/(X2 - X1)
= (\$7,500-\$2,000)/(1,000-200)
= \$5,500/800
= \$6.875 per unit

Fixed Costs       = Y2 - VX2
= \$7,500 - (\$6.875 x 1,000)
= \$625

The cost formula using the high-low method is:

Y = \$625 + \$6.875 (X)

Chapter 3-17
Hansen, Mowen, Elias & Senkow (ITP, 1998)
Utility
Cost               Scatterplot Method
\$8,000

Important: Cost function is only
.
relevant within relevant range
6,000
.
4,000
.        Analyst can fit line
.                  based on his or her
experience
2,000          .
0        200       400      600    800              1,000
Units Produced

Chapter 3-18
Hansen, Mowen, Elias & Senkow (ITP, 1998)

The Method of Least Squares
X       Y         XY         X   2       Y   2

200 \$2,000       400,000           40,000 \$4,000,000
400    2,500   1,000,000          160,000    6,250,000
600    4,500   2,700,000          360,000 20,250,000
800    5,000   4,000,000          640,000 25,000,000
1,000 7,500     7,500,000        1,000,000 56,250,000
3,000 \$21,500 \$15,600,000        2,200,000 \$117,750,000

V = [ XY -  X Y/n]/[ X2 - ( X)2/n]
= 2,700,000/400,000
= \$6.75
The cost formula is:
F =  Y/n-V X/n
= \$21,500/5 - [\$6.75(3,000/5)]
Y = \$250 + \$6.75 (X)
= \$250
Chapter 3-19
Hansen, Mowen, Elias & Senkow (ITP, 1998)

The Method of Least Squares:
Goodness of Fit
R2 (Coefficient of Determination) = V[ XY- X Y/n]/[ Y2- ( Y)2/n]

R2 = .944

R (Coefficient of Correlation) = Square root of R2
= .972

Chapter 3-20
Hansen, Mowen, Elias & Senkow (ITP, 1998)

Product Complexity and
Multiple Drivers

TC = FC +V1C1 + V2C2

Recommended Use of Multiple
Regression

Chapter 3-21
Hansen, Mowen, Elias & Senkow (ITP, 1998)

Cost Behaviour and Managerial
Judgement

Some Tips
   Use past experience
   Try to confirm results with operating personnel
   Use common sense to confirm statistical studies

Chapter 3-22
Hansen, Mowen, Elias & Senkow (ITP, 1998)

Numerical Questions from back
of chapters 2 and 3

W2-3, E2-9, P2-1, P2-9
W3-3, E3-9, P3-1

Chapter 3-23
Hansen, Mowen, Elias & Senkow (ITP, 1998)

Question W2-3

Chapter 3-24
Hansen, Mowen, Elias & Senkow (ITP, 1998)

Question E2-9

Chapter 3-25
Hansen, Mowen, Elias & Senkow (ITP, 1998)

Question P2-1

Chapter 3-26
Hansen, Mowen, Elias & Senkow (ITP, 1998)

Question P2-9

Chapter 3-27
Hansen, Mowen, Elias & Senkow (ITP, 1998)

Question W3-3

Chapter 3-28
Hansen, Mowen, Elias & Senkow (ITP, 1998)

Question E3-9

Chapter 3-29
Hansen, Mowen, Elias & Senkow (ITP, 1998)

Question P3-1

Chapter 3-30
Hansen, Mowen, Elias & Senkow (ITP, 1998)

The End

Chapter 3-31

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